Least Common Multiple (LCM) of 159 and 105
The least common multiple (LCM) of 159 and 105 is 5565.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 159 and 105?
First, calculate the GCD of 159 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 105 = 1 remainder 54 |
| 2 | 105 ÷ 54 = 1 remainder 51 |
| 3 | 54 ÷ 51 = 1 remainder 3 |
| 4 | 51 ÷ 3 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 77 | 13629 |
| 52 and 109 | 5668 |
| 103 and 150 | 15450 |
| 113 and 146 | 16498 |
| 193 and 39 | 7527 |